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United States Patent |
5,061,053
|
Hirakawa
|
October 29, 1991
|
Telephoto zoom lens system
Abstract
A telephoto zoom lens system featuring a zoom ratio on the order of 3 which
uses an inexpensive optical material having a lens refractive index and
which is compact in size can be attained. A first lens group I closest to
the object side has a positive refractive power. The first lens group I
includes a first negative maniscus lens element having a convex surface
directed toward the object and a second positive lens element having a
convex surface with a large curvature directed toward the object. A second
lens group II having a negative refractive power is located on the image
side of the first lens group I. A third lens group III having a positive
refractive power is located on the image side of second lens group II.
Lens group III includes a first lens unit IIIa having a positive
refractive power and a second lens unit IIIb having a positive or negative
refractive power. Zooming is performed by moving the three lens groups
independently of one another along the optical axis. Focusing is performed
by moving the first lens groups along the optical axis. Second lens group
II preferably includes two negative lens elements and one positive lens
element. Lens unit IIIa preferably includes two positive lens elements and
one negative lens element while lens unit IIIb preferably includes a
positive lens and a negative meniscus lens having a convex surface
directed toward the image.
Inventors:
|
Hirakawa; Jun (Tokyo, JP)
|
Assignee:
|
Asahi Kogaku Kogyo K.K. (Tokyo, JP)
|
Appl. No.:
|
363656 |
Filed:
|
June 8, 1989 |
Foreign Application Priority Data
| Jun 08, 1988[JP] | 63-140799 |
Current U.S. Class: |
359/690; 359/745 |
Intern'l Class: |
G02B 009/00 |
Field of Search: |
350/454,455,457,427,423
|
References Cited
U.S. Patent Documents
4815829 | Mar., 1989 | Yamanashi et al. | 350/427.
|
Foreign Patent Documents |
60-60617 | Apr., 1985 | JP.
| |
61-241719 | Oct., 1985 | JP.
| |
0284721 | Dec., 1986 | JP | 350/457.
|
Other References
The Jashin Kogyo, 1988, vol. 12.
|
Primary Examiner: Dzierzynski; Paul M.
Attorney, Agent or Firm: Sughrue, Mion, Zinn, Macpeak & Seas
Claims
What is claimed is:
1. A telephoto zoom lens system comprising, in order from an object side, a
first lens group I having a positive refractive power, a second lens group
II having a negative refractive power, and a third lens group III having a
positive refractive power, wherein zooming is performed by moving the
three lens groups I, II an III independently of one another along an
optical axis, and focusing is performed by moving the first lens group I
along the optical axis, wherein said first lens group I comprises a
two-unit, two-element configuration having a first lens which is a
negative meniscus lens element having a convex surface directed toward the
object, and a second lens which is a positive lens element separated from
said first lens by an air gap and having a convex surface of large
curvature directed toward the object; wherein the second lens group II is
composed of two negative lens elements and one positive lens element; and
wherein said third lens group III includes first and second lens units
IIIa and IIIb in order from the object side, with said first lens unit
having a positive refractive power and consisting of two positive lens
elements and one negative lens element, and said second lens unit IIIb
consisting of a positive lens and a negative meniscus lens having a convex
surface directed toward the image.
2. A telephone lens system according to claim 1, wherein said lens system
satisfies the following conditions:
n.sub.IIIap <1.6 (1)
0.8<.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.<1.2, fII<0(2)
0.8<r.sub.2 /r.sub.3 <1.0 (3)
0.3<r.sub.3 /f.sub.I <0.5 (4)
n.sub.II >1.65 (5)
.nu..sub.IIp <35, .nu..sub.IIn >50 (6)
1.0<f.sub.IIIa /f.sub.III <1.4 (7)
where:
n.sub.IIIap is the average of the refractive indices at the d-line of the
positive lens included in lens unit IIIa;
.DELTA.D.sub.(I-II) is the amount of change in the aerial distance between
the first and second lens groups I and II during zooming;
f.sub.II is the focal length of the second lens group II;
r.sub.2 is the radius of curvature of the image side surface of the first
lens of the first lens group I;
r.sub.3 is the radius of curvature of the object side surface of the second
lens of the first lens group I;
f.sub.I is the focal length of the first lens group I;
n.sub.II is the average of the refractive indices at the d-line of the
lenses of which the second lens group II is composed;
.nu..sub.IIp is the Abbe number of the positive lens included in the second
lens group II;
.nu..sub.IIn is the Abbe number of the negative lens included in the second
lens group II;
f.sub.III is the focal length of the third lens group III; and
f.sub.IIIa is the focal length of the lens unit IIIa.
3. A telephoto lens system according to claim 1, wherein said lens system
satisfies the following conditions:
n.sub.IIIap <1.6 (1)
0.8<.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.<1.2, fII<0(2)
0.8<r.sub.2 /r.sub.3 <1.0 (3)
0.3<r.sub.3 /f.sub.I <0.5 (4)
n.sub.II >1.65 (5)
.nu..sub.IIp <35, .nu..sub.IIn >50 (6)
1.0<f.sub.IIIa /f.sub.III <1.4 (7)
where:
n.sub.IIIap is the average of the refractive indices at the d-line of the
positive lens included in lens unit IIIa;
.DELTA.D.sub.(I-II) is the amount of change in the aerial distance between
the first and second lens groups I and II during zooming;
f.sub.II is the focal length of the second lens group II;
r.sub.2 is the radius of curvature of the image side surface of the first
lens of the first lens group I;
r.sub.3 is the radius of curvature of the object side surface of the second
lens of the first lens group I;
f.sub.I is the focal length of the first lens group I;
n.sub.II is the average of the refractive indices at the d-line of the
lenses of which the second lens group II is composed;
.nu..sub.IIp is the Abbe number of the positive lens included in the second
lens group II;
.nu..sub.IIn is the Abbe number of each negative lens included in the
second lens group II;
f.sub.III is the focal length of the third lens group III; and
f.sub.IIIa is the focal length of the lens unit IIIa.
4. A telephoto lens system according to claim 1, wherein said lens system
satisfies the following conditions:
n.sub.IIIap <1.6 (1)
0.8<.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.<1.2, fII<0(2)
0.8<r.sub.2 /r.sub.3 <1.0 (3)
0.3<r.sub.3 /f.sub.I <0.5 (4)
n.sub.II >1.65 (5)
.nu..sub.IIp <35, .nu..sub.IIn >50 (6)
1.0<f.sub.IIIa /f.sub.III <1.4 (7)
where:
n.sub.IIIap is the average of the refractive indices at the d-line of the
positive lens included in lens unit IIIa;
.DELTA.D.sub.(I-II) is the amount of change in the aerial distance between
the first and second lens groups I and II during zooming;
f.sub.II is the focal length of the second lens group II;
r.sub.2 is the radius of curvature of the image side surface of the first
lens of the first lens group I;
r.sub.3 is the radius of curvature of the object side surface of the second
lens of the first lens group I;
f.sub.I is the focal length of the first lens group I;
n.sub.II is the average of the refractive indices at the d-line of the
lenses of which the second lens group II is composed;
.nu..sub.IIp is the Abbe number of the positive lens included in the second
lens group II;
.nu..sub.IIn is the Abbe number of each negative lens included in the
second lens group II;
f.sub.III is the focal length of the third lens group III; and
f.sub.IIIa is the focal length of the lens unit IIIa.
Description
BACKGROUND OF THE INVENTION
The present invention relates to a photographic zoom lens system, and more
particularly to an inexpensive and compact telephoto zoom lens system that
features a zoom ratio on the order of 3.
A number of telephoto zoom lens systems that feature zoom ratios on the
order of 3 have been proposed in the prior art. For example, JP-A-60-60617
(the term "JP-A" as used herein means an "unexamined published Japanese
patent application") describes a version that is composed of a small
number of lens elements and which is inexpensive, whereas JP-A-61-241719
describes a version that is compact and low in cost.
Although the two prior art versions of zoom lens systems described above
are intended to be available at low cost, they still have problems. The
zoom lens system proposed in JP-A-60-60617 is composed of only eleven
elements but is somewhat bulky due to the zooming method adopted. In
contrast, the version proposed in JP-A-61-241719 adopts a compact zooming
system. However, in order to reduce the number of lens elements to as few
as eleven, an optical material having a high refractive index must be
employed at the penalty of increased cost.
SUMMARY OF THE INVENTION
An object, therefore, of the present invention is to provide a telephoto
zoom lens system that is both inexpensive and compact in size. A more
specific object of the present invention is to provide a zoom lens system
featuring a zoom ratio on the order of 3 that employs fewer lens elements
than previous versions and that uses an inexpensive optical material
having a low refractive index yet is compact in size and ensures
satisfactory performance.
This object of the present invention can generally be attained by a
telephoto zoom lens system that comprises, in order from the object side a
first lens group I having a positive refractive power, a second lens group
II having a negative refractive power, and a third lens group III having a
positive refractive power. This telephoto zoom lens system performs
zooming by moving the three lens groups I, II and III independently of one
another along the optical axis while performing focusing by moving the
first lens group I along the optical axis. More specifically, the first
lens group I is composed of a first lens which is a negative meniscus lens
element having a convex surface directed toward the object, and a second
lens which is a positive lens element having a convex surface of large
curvature directed toward the object. The third lens group III is composed
basically of a first lens unit IIIa having a positive refractive power and
a second lens unit IIIb having a positive or negative refractive power.
The zoom lens system of the present invention satisfies the following
additional conditions:
n.sub.IIIap <1.6 (1)
0.8<.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.<1.2, f.sub.II <0(2)
0.8<r.sub.2 /r.sub.3 <1.0 (3)
0.3<r.sub.3 /f.sub.I <0.5 (4)
n.sub.II >1.65 (5)
.nu..sub.IIp <35, .sub..nu.IIn >50 (6)
1.0<f.sub.IIIa /f.sub.III <1.4
where:
n.sub.IIIap : the average of the refractive indices at the d-line of the
positive lenses included in lens unit IIIa;
.DELTA.D.sub.(I-II) : the amount of change in the aerial distance between
the first and second lens groups I and II during zooming:
f.sub.II : the focal length of the second lens group II;
r.sub.2 : the radius of curvature of the image side surface of the first
lens of first lens group I;
r.sub.3 : the radius of curvature of the object side surface of the second
lens of first lens group I;
f.sub.1 : the focal length of the first lens group I;
n.sub.II : the average of the refractive indices at the d-line of the
lenses of which the second lens group II is composed;
.nu..sub.IIp : the Abbe number of the positive lens included in the second
lens group II;
.nu..sub.IIn : the Abbe number of the negative lens included in the second
lens group II:
f.sub.III : the focal length of the third lens group III; and
f.sub.IIIa : the focal length of the lens unit IIIa.
In a preferred embodiment of the present invention, the second lens group
II is composed of two negative lens elements and one positive lens
element, and the third lens group III is composed of first lens unit IIIa
which consists of two positive lens elements and one negative lens
element, and second lens unit IIIb which consists of a positive lens and a
negative meniscus lens having a convex surface directed toward the image.
BRIEF DESCRIPTION OF THE DRAWINGS
Other features and advantages of the present invention will be apparent
from the following description taken in connection with the accompanying
drawings, wherein:
FIG. 1 is a simplified cross-sectional view of the zoom lens system of
Example 1 when it is at the wide-angle end, with the general manner of
lens movement during zooming also being shown;
FIGS. 3, 5, 7 and 9 are simplified cross-sectional views of the zoom lens
systems of Examples 2, 3, 4 and 5, respectively, when they are at the
wide-angle end;
FIGS. 2A, 4A, 6A, 8A and 10A are graphs plotting the aberration curves
obtained at the wide-angle end with the zoom lens systems of Examples 1,
2, 3, 4 and 5, respectively.
FIGS. 2B, 4B, 6B, 8B and 10B are graphs plotting the aberration curves
obtained at the middle-angle end with the zoom lens systems of Examples 1,
2, 3, 4 and 5, respectively; and
FIGS. 2C, 4C, 6C, 8C and 10C are graphs plotting the aberration curves
obtained at the narrow-angle end with the zoom lens systems of Examples 1,
2, 3, 4 and 5, respectively; and
DETAILED DESCRIPTION OF THE INVENTION
The conditions to be satisfied by the zoom lens system of the present
invention are described hereinafter.
n.sub.IIIap <1.6 (1)
Condition (1) relates to the optical material of which the positive lenses
in lens unit IIIa having a positive refractive power are made. In order to
insure effective compensation for chromatic aberration, positive lenses in
a lens group having a positive power are usually made of an optical
material of a crown glass group having a large Abbe number. For the
purpose of effective compensation for aberrations such as spherical
aberration and coma, higher refractive indices are recommended. However,
the higher the refractive index, the more expensive the crown glass. The
crown glass cannot be too expensive due to the requirement for low cost.
To provide a compromise between these limits condition (1) is set forth.
Using an optical material whose refractive index is higher than the upper
limit defined by condition (1) is not desirable from an economic
viewpoint.
0.8<.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.<1.2, f.sub.II <0(2)
Condition (2) shows the ratio of the change in the distance between the
first and second lens groups I and II during zooming (i.e., the change in
the distance to the object from the second lens group II) with respect to
the focal length of the second lens group II. In other words, this
condition must be satisfied to insure a high zoom ratio. If the lower
limit of condition (2) is not reached because .DELTA.D.sub.(I-II) is too
small or because f.sub.II is too great, the power of the second lens group
II is insufficient to provide a high zoom ratio. If the upper limit of
condition (2) is exceeded because .DELTA.D.sub.(I-II) is too great, the
objective of overall system compactness is not attained. If the upper
limit of condition (2) is exceeded because f.sub.II is too small,
excessive aberrations will occur during zooming. This is certainly not
desirable for the purposes of the present invention.
0.8<r.sub.2 /r.sub.3 <1.0 (3)
0.3<r.sub.3 /f.sub.I <0.5 (4)
Conditions (3) and (4) specify the ranges over which the curvatures of the
opposing surfaces of the first and second lenses in the first lens group I
may vary. According to these conditions, the opposing surfaces of the
first and second lenses assume approximately equal degrees of curvatures,
which may be selected at appropriate values. If r.sub.2 and r.sub.3 differ
so greatly that either the upper limit or the lower limit of condition (3)
is not met, extra-axial performance of the system will be impaired at the
wide-angle end for several reasons including the generation of astigmatism
and lateral chromatic aberration. As a further problem, spherical
aberration cannot be properly compensated for at the narrow-angle end. If
the value of r.sub.3 is so small that the lower limit of condition (4) is
not reached undercompensation of spherical aberration will occur at the
narrow-angle end. If the value of r.sub.3 is so great that the upper limit
of condition (4) is exceeded, overcompensation of spherical aberration
will occur at the narrow-angle end. In either case, the ineffective
compensation cannot be eliminated by the subsequent groups because of the
simplicity in the overall configuration of the system.
n.sub.II >1.65 (5)
.nu..sub.IIp <35, .nu..sub.IIn >50 (6)
Conditions (5) and (6) specify the optical material to be used in the
second lens group II which has a negative refractive power and which is
responsible for zooming action. If the lower limit of condition (5) is not
reached because an optical material having an unduly low refractive index
is used in the second lens group II, the refractive power of the second
lens group II will inevitably become small and its zooming action
accordingly will become insufficient to provide the necessary zoom ratio.
In this connection, it should be noted that keeping the refractive power
by making the curvature strong is not desirable since it will cause great
aberrational variations such as in spherical aberration and astigmatism
during zooming.
Condition (6) is the condition for achromatism of the second lens group II.
If the Abbe numbers of the optical materials used in the second lens group
II are such that condition (6) is not satisfied, achromatism of the second
lens group II is insufficient to prevent variations in chromatic
aberration during zooming. Since these variations cannot be compensated
for by either the first or the third group, it is imperative that
condition (6) be fulfilled.
1.0<f.sub.IIIa /f.sub.III <1.4 (7)
Condition (7) relates to the third lens group III which has the greatest
power of all the components of the system of the present invention. This
condition is necessary to make the third lens group III compact by
designing it as a telephoto lens, thus reducing the overall size of the
lens system. If the power distribution of the third lens group III is out
of balance by an amount such that the lower limit of condition (7) is not
reached, increased chromatic aberration will occur in the lens unit IIIa.
If the upper limit of condition (7) is exceeded, the third lens group III
will become bulky so that the overall size of the lens system is
undesirably large.
Five specific examples of the present invention are described below by way
of illustration, in which: F.sub.NO is an F number; f is a focal length;
is a half view angle; f.sub.B is a back focus; r is the radius of
curvature of an individual lens surface; d is the thickness of a lens or
the aerial distance between two lenses; n is the refractive index of an
individual lens at the d-line; and n is the Abbe number of an individual
lens.
EXAMPLE 1
F.sub.NO =1: 4.1.about.4.8.about.5.6
f=72.00.about.135.01.about.195.00
.omega.=17.2.about.8.9.about.6.2
f.sub.B =39.85.about.52.14.about.65.88
______________________________________
Surface
No. r d n .nu.
______________________________________
1 56.821 2.50 1.80518
25.4
2 39.226 2.04
3 40.890 9.35 1.51633
64.1
4 -194.297 9.25.about. 30.62.about. 37.19
5 -73.745 1.50 1.69680
55.5
6 54.282 2.30
7 -60.886 1.60 1.69680
55.5
8 30.057 3.90 1.80518
25.4
9 409.381 23.68.about. 10.97.about. 3.00
10 65.971 4.46 1.51633
64.1
11 -65.971 0.10
12 43.333 5.51 1.51633
64.1
13 -43.333 1.70 1.80518
25.4
14 -439.612 33.71
15 80.409 4.54 1.58267
46.4
16 -195.051 11.78
17 -26.679 1.70 1.58913
61.2
18 -80.821
______________________________________
n.sub.IIIap =1.51633 (1)
.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.=0.918 (2)
r.sub.2 /r.sub.3 =0.959 (3)
r.sub.3 /f.sub.I =0.372 (4)
n.sub.II =1.733 (5)
.nu..sub.IIp =25.4, .nu..sub.IIn =55.5 (6)
f.sub.IIIa /f.sub.III =1.187 (7)
EXAMPLE 2
F.sub.NO =1: 4.1.about.4.8.about.5.6
f=72.00.about.135.00.about.195.23
.omega.=17.3.about.8.9.about.6.2
f.sub.B =37.40.about.49.82.about.63.70
______________________________________
Surface
No. r d n .nu.
______________________________________
1 58.362 2.50 1.80518
25.4
2 41.035 3.20
3 43.386 9.10 1.48749
70.2
4 -164.730 6.86.about. 31.02.about. 38.52
5 -100.429 1.60 1.69680
55.5
6 20.292 3.80 1.80518
25.4
7 61.557 2.43
8 52.519 1.50 1.69680
55.5
9 138.940 20.35.about. 9.73.about. 3.00
10 107.249 5.00 1.51633
64.1
11 -47.796 0.10
12 44.696 5.36 1.51633
64.1
13 -38.656 1.70 1.80518
25.4
14 -477.928 30.61
15 104.001 3.73 1.63930
44.9
16 -103.204 22.56
17 -29.306 1.70 1.62041
60.3
18 -90.591
______________________________________
n.sub.IIIap =1.51633 (1)
.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.=1.08 (2)
r.sub.2 /r.sub.3 =0.946 (3)
r.sub.3 /f.sub.I =0.3739 (4)
n.sub.II =1.733 (5)
.nu.IIp=25.4, .nu..sub.IIn =55.5 (6)
f.sub.IIIa /f.sub.III =1.347 (7)
EXAMPLE 3
F.sub.NO =1: 4.1.about.4.8.about.5.6
f=72.00.about.135.00.about.195.00
.omega.=17.2.about.8.9.about.6.2
f.sub.B =41.61.about.54.04.about.67.54
______________________________________
Surface
No. r d n .nu.
______________________________________
1 59.960 2.50 1.80518
25.4
2 40.809 2.04
3 42.353 9.35 1.51633
64.1
4 -191.436 8.41.about. 30.45.about. 37.38
5 -74.943 1.50 1.69680
55.5
6 75.209 2.30
7 -77.540 1.60 1.69680
55.5
8 28.203 3.90 1.80518
25.4
9 130.885 25.36.about. 11.59.about. 3.00
10 57.453 6.77 1.51633
64.1
11 -25.515 1.70 1.80518
25.4
12 -46.765 0.10
13 49.391 3.05 1.55963
61.2
14 201.509 33.71
15 108.777 3.60 1.58267
46.4
16 -192.015 10.42
17 -26.088 1.70 1.65830
53.4
18 -65.670
______________________________________
n.sub.IIIap =1.5380 (1)
.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.=0.895 (2)
r.sub.2 /r.sub.3 =0.9635 (3)
r.sub.3 /f.sub.I =0.37 (4)
n.sub.II =1.733 (5)
.nu..sub.IIp =25.4, .nu..sub.IIn =55.5 (6)
f.sub.IIIa /f.sub.III =1.1414 (7)
EXAMPLE 4
F.sub.NO =1: 4.1.about.4.9.about.5.7
f=72.00.about.135.01.about.195.00
.omega.=17.2.about.8.9.about.6.2
f.sub.B =40.46.about.53.29.about.66.58
______________________________________
Surface
No. r d n .nu.
______________________________________
1 63.215 2.50 1.80518
25.4
2 43.227 2.04
3 45.093 9.35 1.51633
64.1
4 -196.091 8.34.about. 31.66.about. 39.26
5 -74.120 1.50 1.69680
55.5
6 74.120 2.30
7 -77.372 1.60 1.69680
55.5
8 28.668 3.90 1.80518
25.4
9 152.463 24.61.about. 11.26.about. 3.00
10 74.250 4.40 1.51633
64.1
11 -74.250 0.10
12 43.576 5.51 1.51633
64.1
13 -43.576 1.70 1.80518
25.4
14 -556.747 27.06
15 111.600 4.54 1.66892
45.0
16 -111.600 17.88
17 -26.480 1.70 1.67790
55.3
18 -75.773
______________________________________
n.sub.IIIap =1.51633 (1)
.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.=0.935 (2)
r.sub.2 /r.sub.3 =0.9586 (3)
r.sub.3 /f.sub.I =0.376 (4)
n.sub.II =1.733 (5)
.nu.II.sub.p =25.4, .nu.IIn=55.5 (6)
f.sub.IIIa /f.sub.III =1.295 (7)
EXAMPLE 5
F.sub.NO= 1: 4.1.about.4.9.about.5.7
f=72.00.about.134.99.about.194.98
.omega.=17.2.about.8.9.about.6.2
f.sub.B =39.71.about.52.39.about.66.38
______________________________________
Surface
No. r d n .nu.
______________________________________
1 58.574 2.50 1.80518
25.4
2 40.482 2.04
3 42.210 9.35 1.51633
64.1
4 -200.346 9.58.about. 31.75.about. 38.62
5 -83.397 1.50 1.69680
55.5
6 53.348 2.30
7 -50.940 1.60 1.69680
55.5
8 29.231 3.90 1.76182
26.6
9 -1107.304 22.97.about. 10.68.about. 3.00
10 67.999 4.46 1.55963
61.2
11 -67.999 0.10
12 43.877 5.37 1.51633
64.1
13 -43.877 1.70 1.80518
25.4
14 -982.958 33.71
15 77.360 4.54 1.55690
48.6
16 -146.348 12.50
17 -26.991 1.70 1.58913
61.2
18 -89.841
______________________________________
n.sub.IIIap =1.5380 (1)
.vertline..DELTA.D.sub.(I-II) /f.sub.II .vertline.=0.951 (2)
r.sub.2 /r.sub.3 =0.959 (3)
r.sub.3 /f.sub.I =0.373 (4)
n.sub.II =1.718 (5)
.nu..sub.IIp =26.6, .nu..sub.IIn =55.5 (6)
f.sub.IIIa /f.sub.III =1.205 (7)
As described in the foregoing pages, the telephoto zoom lens system
contemplated by the present invention is of a type that features a zoom
ratio on the order of 3. By satisfying conditions (1) to (7) set forth
hereinabove, this zoom lens system offers various advantages. It can be
constructed of an inexpensive optical material, may be composed of a small
number of components and hence features compactness and in spite of its
compact size, the lens system of the present invention insures
satisfactory performance as will be apparent from the aberration curves
plotted in FIGS. 2, 4, 6, 8 and 10.
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